Let's assume the amount invested in bonds paying 12% interest is x dollars, and the amount invested in certificates of deposit paying 51% interest is y dollars.
According to the given information, the total amount invested is $21,000, so we have the equation:
x + y = 21,000
The annual income from these investments is $2250, which can be expressed as the sum of the interest earned from each investment:
0.12x + 0.51y = 2250
Now, we have a system of two equations:
x + y = 21,000
0.12x + 0.51y = 2250
We can solve this system of equations to find the values of x and y, representing the amounts invested in bonds and certificates of deposit, respectively.
One way to solve this system is by substitution or elimination. In this case, let's use the elimination method:
Multiplying the first equation by 0.12 to make the coefficients of x in both equations the same, we have:
0.12x + 0.12y = 2520
Subtracting this equation from the second equation, we eliminate x:
0.51y - 0.12y = 2250 - 2520
0.39y = -270
y = -270 / 0.39
y ≈ -692.31
Since we cannot have a negative investment, this suggests an error or inconsistency in the given information or calculations.
Please double-check the provided values or calculations, as they currently do not yield a feasible solution.